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2007 Solutions for the Constant Quantum Yang-Baxter Equation From Lie (Super) Algebras
Adrian Tanasă, Ángel Ballesteros, Francisco J. Herranz
J. Geom. Symmetry Phys. 10: 83-91 (2007). DOI: 10.7546/jgsp-10-2007-83-92


We present a systematic procedure to obtain singular solutions of the constant quantum Yang-Baxter equation in arbitrary dimension. This approach, inspired by the Lie (super)algebra structure, is explicitly applied to the particular case of (graded) contractions of the orthogonal real algebra ${\mathfrak{so}}(N+1)$. In this way we show that “classical” contraction parameters which appear in the commutation relations of the contracted Lie algebras, become quantum deformation parameters, arising as entries of the resulting quantum $R$-matrices.


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Adrian Tanasă. Ángel Ballesteros. Francisco J. Herranz. "Solutions for the Constant Quantum Yang-Baxter Equation From Lie (Super) Algebras." J. Geom. Symmetry Phys. 10 83 - 91, 2007.


Published: 2007
First available in Project Euclid: 20 May 2017

zbMATH: 1143.81307
MathSciNet: MR2380052
Digital Object Identifier: 10.7546/jgsp-10-2007-83-92

Rights: Copyright © 2007 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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